Generally, this invention relates to plant transplant apparatus and methods for transplanting propagules (or plants) in order to improve transplanting yield and/or survivability of transplanted plants and in order to increase the efficiency of the transplant process and reduce processing and related waste. Some embodiments of this invention relate to an operational system for transplanting growing plants that may improve operational functions to maximize transplant yields. In particular, the invention discloses a plant transplanter whose punch pins, or, more generally, plant punch elements, may be user-detachable, so that plant punch elements of a certain design may be installed as part of the machine in order to customize the transplant process for a given application (such as, e.g., the transplanting of a certain species of plant for distribution in a certain geographic location). Such customization for a certain application allows for improvement of transplant yields and/or survivability of transplanted plants. The invention also relates to a plant transplanter that uses at least one plant punch element that is designed (with, e.g., a convex head surface shape) to forcibly push to the side a plant to be transplanted during a transplanting event, resulting in less crushing damage to the transplanted plant and a less intrusive plant punch, and thereby resulting in increased plant yields and/or survivability. The invention further discloses a propagule container tray that is areally continuous (e.g., exhibits an unclustered arrangement of propagule plug containers (or propagule transplant containers)), and that, when used in a plant punch machine (or more generally a plant transplanter), is operationally compatible with a numerically significant number of alternative adolescent plant tray configurations. The invention also provides for a consultable collection (such as printed documents arranged in binder or book, or an electronic database stored on a computer, as but a few examples) of plant transplant process information (such as, e.g., a recommended plant punch element assembly selection for a given propagule container tray configuration and a given adolescent plant tray configuration) combinations. Embodiments of the invention may be viewed as focusing upon techniques and processes that may improve transfer of plant seedlings from a high-density tray to a larger/lower density tray to maximize transplant yields which may in turn decrease production costs and may also increase profits.